In my view, Bittrex is the most trustworthy exchange out there. In an article posted on the official channels, they announced their stance on the upcoming fork.
If you have a Bitcoin (BTC) balance on Bittrex during the BCC UAHF time on August 1st, 5:20am (12:20pm UTC), you will be credited the equivalent amount of Bitcoin Cash (BCC) on a 1:1 basis. i.e. 1 BTC on Bittrex held during the on-exchange snapshot will get you 1 BCC.
This is good news for people who do not want to move their coins off of the exchange into a private wallet. It also gives people an opportunity to buy in to cheap alts quickly; most alts are bleeding as people flock to btc to get BitCoin Cash. Why they want BCC is beyond me . . . If everyone is moving their coins to get the new one, what will happen to the price once it starts trading? It will plummet.
Trex has been pretty reliable, and if they say they are going to do something, I believe them. What am I doing to prepare? I've moved a decent sized portion of my funds off of exchanges and into a personal wallet. Not really because I want the BCC, I'll take them don't get me wrong, but I like having access to my money at ALL times. Bitcoin deposits and withdrawals will be frozen August 1st.
I'm leaving some on the exchange to capitalize on the huge sell off that is occurring now. Once these people have received their coins, I believe a lot of them will go back into alts, driving back up the price.
BCC may not be actively traded on Bittrex after the fork, but I'm betting that they will add it soon after.
There is no guarantee that any markets will open to allow BCC assets to be tradable on Bittrex exchange.